Data processing method, equalizer and receiver
The invention is related to an equalizer comprising, for instance: means for creating a first covariance matrix and defining a Cholesky decomposition matrix of an inverse matrix of the first covariance matrix, means for removing selected covariance components from the Cholesky decomposition matrix, means for computing the inverse of a sub-matrix, which represents the common part of the first covariance matrix and a second covariance matrix, which includes covariance estimates of a second observation time, by using the aid of the Cholesky decomposition of the inverse matrix of the first covariance matrix, means for estimating interference from a received signal at a second observation time and determining additional covariance components on the basis of the estimation and means for creating the Cholesky decomposition of the inverse matrix of the second covariance matrix by using unitary rotations.
The invention relates to a data processing method in an equalizer of a receiver, an equalizer and a receiver.
BACKGROUNDTransmissions through multi-path channels usually experience inter-symbol interference at a receiver. One of the methods to mitigate the interference is to utilise an equalizer at the receiver to compensate for channel distortion.
Iterative turbo methods have been used for channel equalization where a channel equalizer and a channel decoder exchange information iteratively. One of the methods consists of a soft interference canceller followed by a Minimum mean-square error MMSE filter (SC/MMSE) optimised with the channel decoder feedback, channel response and noise level.
The dominating computational complexity of the SC/MMSE algorithm lies in the computation of the inverse of the interference covariance matrix. The inverse is calculated for each transmitted symbol in the received signal.
BRIEF DESCRIPTION OF THE INVENTIONAccording to an aspect of the invention, there is provided a data processing method in a channel equalizer of a receiver, comprising: estimating interference from a received signal at a first observation time, creating a first covariance matrix on the basis of the estimation and defining an inverse matrix of the first covariance matrix and a Cholesky decomposition matrix thereof, removing selected covariance components from the Cholesky decomposition matrix, computing the inverse of a sub-matrix, which represents the common part of the first covariance matrix, and a second covariance matrix, which includes covariance estimates of a second observation time, by using the aid of the Cholesky decomposition of the inverse matrix of the first covariance matrix, estimating interference from a received signal at a second observation time and determining additional covariance components on the basis of the estimation, creating the Cholesky decomposition of the inverse matrix of the second covariance matrix by using unitary rotations, generating an output value of the channel equalizer by utilizing information obtained with the aid of the Cholesky decomposition of the inverse matrix of the second covariance matrix.
According to another aspect of the invention, there is provided an equalizer comprising: means for estimating interference from a received signal at a first observation time, creating a first covariance matrix on the basis of the estimation and defining an inverse matrix of the first covariance matrix and a Cholesky decomposition matrix thereof, means for removing selected covariance components from the Cholesky decomposition matrix, means for computing the inverse of a sub-matrix, which represents the common part of the first covariance matrix, and a second covariance matrix, which includes covariance estimates of a second observation time, by using the aid of the Cholesky decomposition of the inverse matrix of the first covariance matrix, means for estimating interference from a received signal at a second observation time and determining additional covariance components on the basis of the estimation, means for creating the Cholesky decomposition of the inverse matrix of the second covariance matrix by using unitary rotations, means for generating an output value of the channel equalizer by utilizing information obtained with the aid of the Cholesky decomposition of the inverse matrix of the second covariance matrix.
According to another aspect of the invention, there is provided a receiver comprising: means for estimating interference from a received signal at a first observation time, creating a first covariance matrix on the basis of the estimation and defining an inverse matrix of the first covariance matrix and a Cholesky decomposition matrix thereof, means for removing selected covariance components from the Cholesky decomposition matrix, means for computing the inverse of a sub-matrix, which represents the common part of the first covariance matrix, and a second covariance matrix, which includes covariance estimates of a second observation time, by using the aid of the Cholesky decomposition of the inverse matrix of the first covariance matrix, means for estimating interference from a received signal at a second observation time and determining additional covariance components on the basis of the estimation, means for creating the Cholesky decomposition of the inverse matrix of the second covariance matrix by using unitary rotations, means for generating an output value of the channel equalizer by utilizing information obtained with the aid of the Cholesky decomposition of the inverse matrix of the second covariance matrix.
According to another aspect of the invention, there is provided an equalizer configured to: estimate interference from a received signal at a first observation time, creating a first covariance matrix on the basis of the estimation and defining an inverse matrix of the first covariance matrix and a Cholesky decomposition matrix thereof, remove selected covariance components from the Cholesky decomposition matrix, compute the inverse of a sub-matrix, which represents the common part of the first covariance matrix, and a second covariance matrix, which includes covariance estimates of a second observation time, by using the aid of the Cholesky decomposition of the inverse matrix of the first covariance matrix, estimate interference from a received signal at a second observation time and determining additional covariance components on the basis of the estimation, create the Cholesky decomposition of the inverse matrix of the second covariance matrix by using unitary rotations, generate an output value of the channel equalizer by utilizing information obtained with the aid of the Cholesky decomposition of the inverse matrix of the second covariance matrix.
According to another aspect of the invention, there is provided a receiver configured to: estimate interference from a received signal at a first observation time, creating a first covariance matrix on the basis of the estimation and defining an inverse matrix of the first covariance matrix and a Cholesky decomposition matrix thereof, remove selected covariance components from the Cholesky decomposition matrix, compute the inverse of a sub-matrix, which represents the common part of the first covariance matrix, and a second covariance matrix, which includes covariance estimates of a second observation time, by using the aid of the Cholesky decomposition of the inverse matrix of the first covariance matrix, estimate interference from a received signal at a second observation time and determining additional covariance components on the basis of the estimation, create the Cholesky decomposition of the inverse matrix of the second covariance matrix by using unitary rotations, generate an output value of the channel equalizer by utilizing information obtained with the aid of the Cholesky decomposition of the inverse matrix of the second covariance matrix.
Embodiments of the invention are described in the dependent claims.
The method and system of the invention provide several advantages. An embodiment of the invention offers an efficient method for computing a matrix inversion in an equalizer. The embodiment can be implemented by a pipelined, parallel arrangement with, for instance, one or more systolic arrays.
LIST OF DRAWINGSIn the following, the invention will be described in greater detail with reference to the embodiments and the accompanying drawings, in which
With reference to
It is clear to a person skilled in the art that the method according to the invention can be applied to systems utilizing different modulation methods or air interface standards.
The cellular radio system can also communicate with other networks, such as a public switched telephone network or the Internet.
It is possible to apply the turbo principle to many detection/decoding problems such as channel estimation, channel equalization, detection of coded modulation, multi-user detection and channel decoding. The example depicted here in further detail in
The equalizer depicted as an example here, comprises a soft interference canceller (SC) followed by an MMSE filter (Minimum-Mean-Square Equalizer) optimised with the channel decoder feedback, channel response and noise level. The SC/MMSE equalizer uses information on transmitted bits.
The principle of turbo equalization applied to the usage of SC/MMSE algorithm leads to a structure where the likelihood information is exchanged between SC/MMSE equalizer and a decoder through the interleaving/de-interleaving blocks. The SC/MMSE turbo receiver structure can be applied not only the equalization of inter-symbol interference for single-carrier signalling but also to various other signalling schemes, such as multiple signal detection in multiple-input-multiple-output (MIMO) systems.
An example of the SC/MMSE turbo receiver structure is shown in
The decoder 204 can in general be any algorithm capable of providing soft symbol information metrics also called symbol decisions, data decisions or symbol estimates, for instance. Possible decoder algorithms are, for instance, log-domain maximum-a-posteriori (log-MAP), its max-approximation (max-log-MAP) and the soft-output Viterbi algorithm (SOVA).
The embodiment of a data processing method in a channel equalizer of a receiver utilises the fact that two consecutive covariance matrices called in this application a first covariance matrix and a second covariance matrix include mostly the same components. The second covariance matrix at the time n+1 is a shifted version of the previous (first) covariance matrix at the time n with new components only in the last row and column. The approach is especially useful in MIMO systems, where multiple desired symbol likelihood information is computed with a common interference covariance matrix but different channel responses. The equalizer operates with a sliding signal window, and the interference cancelled signal covariance matrix can be recursively updated by exploiting the knowledge of the memory within the sliding window. The size of a sliding step is usually one.
Typically, as far as the equalizing process continues, the sliding of the signal window continues and the inversion of a new covariance matrix is calculated with the aid of the previous inverse covariance matrix utilising common covariance components.
In cases where the received signal is over-sampled in space or time, the covariance matrix has a block structure. The recursion must then be executed multiple times per each equalized symbol to match the over-sampling ratio.
The embodiment begins in block 300. The embodiment is suitable especially for systems where multiple antennas transmit a coded and interleaved signal, which is received with one of multiple antennas. In block 302, interference in a radio channel is estimated. The interference estimation is known in the art and it is therefore not explained here in further detail. One widely used method is measuring the impulse response of a received signal. If there are several radio channels of interest, the interference is usually estimated in these channels. In a multi-user system, the interference can be estimated for every user in a multi-user system or a common interference estimate is used. In the example used here, the received signal is modelled with the linear model:
r=Hb+w, (1)
-
- where
- H is a channel response matrix,
- b is a symbol vector,
- w is a noise vector.
On the basis of the interference estimation, a first covariance matrix is created. The size of the matrix depends on the amount of receiver sampling and the channel response length. The system may be a MIMO (Multiple input, multiple output) system, in which case there are several simultaneous radio transmissions to be received through different channels.
In block 302, an inverse matrix of the first covariance matrix and its Cholesky decomposition are also defined. The inverse matrix of the first covariance matrix can be calculated using exhaustive calculation used in prior art equalizers or another prior art method.
The inverse matrix of the first covariance matrix can be partitioned as follows:
-
- where
- up means a scalar,
- up means a vector,
- upH means a complex-conjugate transpose vector,
- Up means a sub-matrix and
- H means a complex-conjugate transpose (Hermitian) matrix.
The Cholesky decomposition of the partitioned inverse matrix (2) is defined as a lower-triangular matrix:
-
- where
- ωp means a scalar,
- ωp means a vector,
- {overscore (o)}H means a zero vector and
- Ωp means a lower triangular sub-matrix,
- H means a complex-conjugate transpose (Hermitian) matrix.
In block 304, selected covariance components are removed from the Cholesky decomposition matrix. The covariance components to be removed are typically components related to the observation time of the previous covariance matrix.
In block 306, the inverse of the sub-matrix {overscore (Σ)} is computed. The sub-matrix Z represents the common part of the first covariance matrix and a second covariance matrix, which includes covariance estimates of a second observation time, by using the aid of the Cholesky decomposition of the inverse matrix of the first covariance matrix.
Two consecutive covariance matrices called in this application a first covariance matrix and a second covariance matrix include mostly the same components. The second covariance matrix at the time n+1 is a shifted version of the previous (first) covariance matrix at the time n with new components only in the last row and column.
The sub-matrix {overscore (Σ)} representing the common part of the two consecutive covariance matrices is clarified with the aid of
The Cholesky factorisation of the inverse matrix {overscore (Σ)}−1 can be computed as:
{overscore (Σ)}−1={overscore (ΩΩ)}H, (4)
-
- where
- {overscore (Ω)} is a sub-matrix and
- {overscore (Ω)}H is a complex-conjugate transpose of the sub-matrix.
We find that
{overscore (Ω)}=Ωp, (5)
-
- where
- Ωp is a sub-matrix of (3).
In block 308, interference from a received signal is estimated at a second observation time and additional covariance components are determined on the basis of the estimation. The additional covariance components are the covariance components of the part of the second covariance matrix 402 of
Hence the additional covariance components can be computed as
-
- where
- σƒ means covariance component vector,
- σƒ means covariance component (scalar) (located in the corner of the second covariance matrix),
- H(n) means system matrix in the observation time of the second covariance matrix,
- diag means a diagonal matrix,
- {circumflex over (b)}(n) is a symbol estimate,
- H means a complex conjugate (Hermitian) matrix,
- σ02 is the noise variance,
- I is an interference matrix.
The computation of new covariance components in (6) is defined for BPSK modulation. The extension of the computation to other modulation methods can be implemented by known methods.
In block 310, Cholesky decomposition of the inverse matrix of the second covariance matrix is created by using unitary rotations.
The Cholesky factorisation of the inverse matrix of the second covariance matrix is defined as a lower-triangular matrix:
-
- where
- Ωƒ means a lower triangular sub-matrix,
- ωƒH means a vector,
- {overscore (o)}H means a zero vector,
- ωƒ* means a scalar,
- H means a complex-conjugate transpose (Hermitian) matrix and
- * means a complex-conjugate.
A pre-array is composed with the additional covariance components σƒ, σƒ which are pre-processed with the prior sub-matrix {overscore (ω)}. By unitary rotations, it is possible to iteratively annihilate the last column of the pre-array. If the dimension of the matrix Wƒ is d, d−1 rotations are needed to annihilate all but the last element of the last column of the pre-array. Thus the Cholesky factorisation of the inverse matrix of the second covariance matrix can be expressed with the pre-array and a concatenated rotation matrix as:
-
- where
- {overscore (ω)}means a sub-matrix,
- {overscore (o)}H means a zero vector,
- {overscore (ω)}H means a complex-conjugate transpose of the sub-matrix,
uƒ=(σƒ−σƒH{overscore (ωω)}Hσƒ), - σf means covariance component (scalar),
- Θ means series of unitary rotations and
- H means a complex-conjugate transpose (Hermitian) matrix.
Algorithms based on unitary rotation are well-suited for pipelined and parallel implementations with, for instance, systolic arrays.
In block 312, an output value of the channel equalizer is generated by utilizing information obtained with the aid of the Cholesky decomposition of the inverse matrix of the second covariance matrix. The output value of the channel equalizer is typically generated by further utilizing a-priori symbol estimate information. The a-priori symbol estimate information may include, for instance, symbol decisions (also called, for instance, likelihood information, symbol estimate, data decision).
The output of an equalizer can be defined as:
zk(n)=βk(n)(αk(n){overscore (b)}k(n)+ηkH(n)WƒH{tilde over (r)}(n)), (9)
-
- where
αk(n)=ηkH(n)ηk(n), (10)
ηk(n)=WƒHhk(n), (11)
- hk(n) is a channel response vector,
- n means an nth symbol,
- H means a complex-conjugate transpose (Hermitian) matrix,
- {circumflex over (b)}k(n) is a symbol estimate (or a symbol decision, likelihood information, symbol estimate or a data decision) based on a channel decoder feedback,
- Wf is defined in the form (8),
{tilde over (r)}(n)=r(n)−{circumflex over (b)} (13) - where
- k(n) is a channel response matrix and
- n means an nth symbol.
- where
The computation in (9)-(12) is defined for BPSK modulation. The extension of the computation to other modulation methods can be carried out by known methods
The embodiment ends in block 314. Arrow 316 depicts that the embodiment may be repeated for calculating the next equalizer output signal value usually for the next transmitted symbol.
In
Channel matrix is estimated with a channel estimator and required channel response values hk are conveyed from block 502 to block 500 along with new (additional) covariance matrix components σƒ, σƒ. In block 500 the Cholesky factorisation of the inverse matrix of the second covariance matrix is calculated according to equation (8). The output values of the block 500 are the vectors η□k and WƒH{tilde over (r)} where ( )H means complex-conjugate transpose and is {tilde over (r)}(n)=r(n)−H{circumflex over (b)}, which means a received signal from where known signal components have been removed.
In multiplier 504, ηk(n) and WƒH{tilde over (r)}(n) are multiplied element-wise. Squaring block 506 and adder 510 correspond to the calculation of ηkH(n)ηk(n), which gives αk(n) according to equation (10).
In multiplier 514, αk(n) is multiplied with {circumflex over (b)}k(n), which is a symbol estimate based on channel decoder 204 feedback depicted in
In block 518, βk(n) is calculated according to equation (12). The output of the adder 512 and βk(n) are multiplied in multiplier 516 and the output of the equalizer is then zk(n)=βk(n)(αk(n){circumflex over (b)}k(n)+ηkH(n)WƒH{tilde over (r)}(n)) according to equation (9). When multiple transmitters are received, hk(n), ηk, αk(n) βk(n) and zk(n) must be computed separately for each transmitter.
The equalizer 608 carries out most processing steps of embodiments of the data processing method. The structure of the block is described in
The embodiments of the data processing method are typically implemented as a processor and software, but different hardware implementations are also feasible, e.g. a circuit built of separate logics components or one or more client-specific integrated circuits (Application-Specific Integrated Circuit, ASIC). A hybrid of these implementations is also feasible. Additionally, unitary rotations can be implemented with systolic arrays.
Even though the invention is described above with reference to an example according to the accompanying drawings, it is clear that the invention is not restricted thereto but it can be modified in several ways within the scope of the appended claims.
Claims
1. A data processing method in a channel equalizer of a receiver, the method comprising:
- estimating interference from a received signal at a first observation time, creating a first covariance matrix on the basis of the estimation and defining an inverse matrix of the first covariance matrix and a Cholesky decomposition matrix;
- removing selected covariance components from the Cholesky decomposition matrix;
- computing the inverse of a sub-matrix, which represents the common part of the first covariance matrix and a second covariance matrix, which includes covariance estimates of a second observation time, by using the aid of the Cholesky decomposition of the inverse matrix of the first covariance matrix;
- estimating interference from a received signal at a second observation time and determining additional covariance components on the basis of the estimation;
- creating the Cholesky decomposition of the inverse matrix of the second covariance matrix by using unitary rotations; and
- generating an output value of the channel equalizer by utilizing information obtained with the aid of the Cholesky decomposition of the inverse matrix of the second covariance matrix.
2. The method of claim 1, further comprising means for filtering additional covariance components.
3. The method of claim 1, further defining the Cholesky decomposition of the inverse matrix of the first covariance matrix of the form W p = ( ω p o _ H ω p Ω p ),
- where ωp is a scalar, ωp is a vector, {overscore (o)}H is a zero vector and Ωp is a lower triangular sub-matrix.
4. The method of claim 1, further comprising the step of partitioning the inverse matrix of the first covariance matrix as U ( n ) = ( u p u p H u p U p ),
- wherein up is a scalar, up is a vector, upH is a complex-conjugate transpose vector, Up is a sub-matrix and H is a complex-conjugate transpose matrix.
5. The method of claim 1, wherein the selection of the covariance components to be removed is based on the size of the sliding step of a signal window.
6. The method of claim 1, further comprising the steps of determining additional covariance components as ( σ f σ f ) = ( H ( n ) [ diag ( 1 - b ^ 2 ( n ) ) ] H H ( n ) + I δ 0 2 ) ( 0 1 ),
- wherein σƒ is covariance component vector, σƒ is a covariance component located in the corner of the second covariance matrix, H(n) is a system matrix in the observation time of the second covariance matrix, diag is a diagonal matrix, {circumflex over (b)}(n) is a symbol estimate, H is a complex conjugate matrix, σ02 is the noise variance, and I is an interference matrix.
7. The method of claim 1, further comprising the step of defining the computation of the inverse of the sub-matrix {overscore (Σ)} representing the common part of the two consecutive covariance matrices with the aid of determination {overscore (Σ)}−1={overscore (ΩΩ)}H, wherein {overscore (Ω)} is a sub-matrix and {overscore (Ω)}H is a complex-conjugate transpose of the sub-matrix.
8. The method of claim 1, further comprising the step of defining Cholesky factorisation of the inverse matrix of the second covariance matrix as W f = ( Ω _ - u f ΩΩ _ H σ f o _ H u f ) Θ,
- wherein {overscore (Ω)} is a sub-matrix, {overscore (o)}H is a zero vector, {overscore (Ω)}H is a complex-conjugate transpose of the sub-matrix, uƒ=(σƒ−σƒH{overscore (ΩΩ)}Hσƒ), σf is a covariance component, Θ is a series of unitary rotations and H is a complex-conjugate transpose matrix.
9. The method of claim 1, wherein an output signal of an equalizer is generated as follows: z k ( n ) = β k ( n ) ( α k ( n ) b ^ k ( n ) + η k H ( n ) W f H r ~ ( n ) ) wherein α k ( n ) = η k H ( n ) η k ( n ), η k ( n ) = W f H h k ( n ), β k ( n ) = 1 - α k ( n ) α k ( n ) + b ^ k ( n ) - 2, hk(n) is a channel response vector, n is an nth symbol, H is a complex-conjugate transpose matrix, {circumflex over (b)}k(n) is a symbol estimate based on a channel decoder feedback, W f = ( Ω _ - u f Ω _ Ω _ H σ f o _ H u f ) Θ wherein {overscore (Ω)}is a sub-matrix, {overscore (o)}H is a zero vector, {overscore (Ω)}H is a complex-conjugate transpose of the sub-matrix, uƒ=(σƒ−σƒH{overscore (ΩΩ)}Hσƒ), σf is a covariance component, Θ is a series of unitary rotations and H is a complex-conjugate transpose matrix, {tilde over (r)}(n)=r(n)=H{circumflex over (b)} where Hk(n) is a channel response matrix and n means an nth symbol.
10. The method of claim 1, wherein the output value of the channel equalizer is generated by further utilizing a-priori symbol estimate information.
11. An equalizer comprising:
- means for estimating interference from a received signal at a first observation time, creating a first covariance matrix on the basis of the estimation and defining an inverse matrix of the first covariance matrix and a Cholesky decomposition matrix;
- means for removing selected covariance components from the Cholesky decomposition matrix;
- means for computing the inverse of a sub-matrix, which represents the common part of the first covariance matrix and a second covariance matrix, which includes covariance estimates of a second observation time, by using the aid of the Cholesky decomposition of the inverse matrix of the first covariance matrix;
- means for estimating interference from a received signal at a second observation time and determining additional covariance components on the basis of the estimation;
- means for creating the Cholesky decomposition of the inverse matrix of the second covariance matrix by using unitary rotations; and
- means for generating an output value of the channel equalizer by utilizing information obtained with the aid of the Cholesky decomposition of the inverse matrix of the second covariance matrix.
12. The equalizer of claim 11, wherein the Cholesky decomposition of the inverse matrix of the first covariance matrix is of the form W p = ( ω p o _ H ω p Ω p ),
- where ωp is a scalar, ωp is a vector, {overscore (o)}H is a zero vector and Ωp is a lower triangular sub-matrix.
13. The equalizer of claim 11, wherein the inverse matrix of the first covariance matrix is partitioned as U ( n ) = ( u p u p H u p U p ),
- wherein up is a scalar, up is a vector, upH is a complex-conjugate transpose vector, Up is a sub-matrix and H is a complex-conjugate transpose matrix.
14. The equalizer of claim 11, wherein the selection of the covariance components to be removed is based on the size of the sliding step of the signal window.
15. The equalizer of claim 11, wherein additional covariance components are determined as ( σ f σ f ) = ( H ( n ) [ diag ( 1 - b ^ 2 ( n ) ) ] H H ( n ) + I δ 0 2 ) ( 0 1 ),
- wherein σƒ is covariance component vector, σf is a covariance component located in the corner of the second covariance matrix, H(n) is a system matrix in the observation time of the second covariance matrix, diag is a diagonal matrix, {circumflex over (b)}(n) is a symbol estimate, H is a complex conjugate matrix, σ02 is the noise variance, and I is an interference matrix.
16. The equalizer of claim 11, wherein the computation of the inverse of the sub-matrix {overscore (Σ)} representing the common part of the two consecutive covariance matrices is defined with the aid of determination {overscore (Σ)}−1={overscore (ΩΩ)}H, wherein {overscore (Ω)} is a sub-matrix and {overscore (Ω)}H is a complex-conjugate transpose of the sub-matrix.
17. The equalizer of claim 11, wherein Cholesky factorisation of the inverse matrix of the second covariance matrix is defined as W f = ( Ω _ - u f Ω _ Ω _ H σ f o _ H u f ) Θ,
- wherein {overscore (Ω)} is a sub-matrix, {overscore (o)}H is a zero vector, {overscore (Ω)}H is a complex-conjugate transpose of the sub-matrix, uƒ=(σƒ−σƒH{overscore (ΩΩ)}Hσƒ), θf is a covariance component, Θ is a series of unitary rotations and H is a complex-conjugate transpose matrix.
18. The equalizer of claim 11, wherein an output signal of an equalizer is generated as z k ( n ) = β k ( n ) ( α k ( n ) b ^ k ( n ) + η k H ( n ) W f H r ~ ( n ) ), wherein α k ( n ) = η k H ( n ) η k ( n ), η k ( n ) = W f H h k ( n ), β k ( n ) = 1 - α k ( n ) α k ( n ) + b ^ k ( n ) - 2, hk(n) is a channel response vector, n is an nth symbol, H is a complex-conjugate transpose matrix, {circumflex over (b)}k(n) is a symbol estimate based on a channel decoder feedback, W f = ( Ω _ - u f Ω _ Ω _ H σ f o _ H u f ) Θ wherein {overscore (Ω)} is a sub-matrix, {overscore (o)}H is a zero vector, {overscore (Ω)}H is a complex-conjugate transpose of the sub-matrix, uƒ=(σƒ−σƒ{overscore (ΩΩ)}Hσƒ), σf is a covariance component, Θ is a series of unitary rotations and H is a complex-conjugate transpose matrix, {tilde over (r)}(n)=r(n)−H{tilde over (b)} where Hk(n) is a channel response matrix and n means an nth symbol.
19. The equalizer of claim 11, further comprising means for generating the output value of the channel equalizer by further utilizing a-priori symbol estimate information.
20. A receiver comprising:
- means for estimating interference from a received signal at a first observation time, creating a first covariance matrix on the basis of the estimation and defining an inverse matrix of the first covariance matrix and a Cholesky decomposition matrix;
- means for removing selected covariance components from the Cholesky decomposition matrix;
- means for computing the inverse of a sub-matrix, which represents the common part of the first covariance matrix and a second covariance matrix, which includes covariance estimates of a second observation time, by using the aid of the Cholesky decomposition of the inverse matrix of the first covariance matrix;
- means for estimating interference from a received signal at a second observation time and determining additional covariance components on the basis of the estimation;
- means for creating the Cholesky decomposition of the inverse matrix of the second covariance matrix by using unitary rotations; and
- means for generating an output value of the channel equalizer by utilizing information obtained with the aid of the Cholesky decomposition of the inverse matrix of the second covariance matrix.
21. An equalizer configured to:
- estimate interference from a received signal at a first observation time, creating a first covariance matrix on the basis of the estimation and defining an inverse matrix of the first covariance matrix and a Cholesky decomposition matrix;
- remove selected covariance components from the Cholesky decomposition matrix;
- compute the inverse of a sub-matrix, which represents the common part of the first covariance matrix and a second covariance matrix, which includes covariance estimates of a second observation time, by using the aid of the Cholesky decomposition of the inverse matrix of the first covariance matrix;
- estimate interference from a received signal at a second observation time and determining additional covariance components on the basis of the estimation;
- create the Cholesky decomposition of the inverse matrix of the second covariance matrix by using unitary rotations; and
- generate an output value of the channel equalizer by utilizing information obtained with the aid of the Cholesky decomposition of the inverse matrix of the second covariance matrix.
22. A receiver configured to:
- estimate interference from a received signal at a first observation time, creating a first covariance matrix on the basis of the estimation and defining an inverse matrix of the first covariance matrix and a Cholesky decomposition matrix;
- remove selected covariance components from the Cholesky decomposition matrix;
- compute the inverse of a sub-matrix, which represents the common part of the first covariance matrix and a second covariance matrix, which includes covariance estimates of a second observation time, by using the aid of the Cholesky decomposition of the inverse matrix of the first covariance matrix;
- estimate interference from a received signal at a second observation time and determining additional covariance components on the basis of the estimation;
- create the Cholesky decomposition of the inverse matrix of the second covariance matrix by using unitary rotations; and
- generate an output value of the channel equalizer by utilizing information obtained with the aid of the Cholesky decomposition of the inverse matrix of the second covariance matrix.
Type: Application
Filed: Mar 25, 2004
Publication Date: Aug 11, 2005
Patent Grant number: 7492844
Inventors: Kimmo Kansanen (Oulu), Tadashi Matsumoto (Oulu)
Application Number: 10/808,554